Steering Criteria via Covariance Matrices of Local Observables in Arbitrary Dimensional Quantum Systems

TL;DR

This paper introduces new steerability criteria for quantum systems of any dimension using covariance matrices of local observables, enabling detection of entanglement especially in high-dimensional and continuous-variable systems.

Contribution

It develops a unified approach to steerability detection applicable to finite and infinite-dimensional systems, extending Gaussian criteria and avoiding complex numerical optimization.

Findings

Criteria are effective for high-dimensional entangled states

Applicable to both finite and infinite-dimensional systems

No numerical optimization needed for certain criteria

Abstract

We derive steerability criteria applicable for both finite and infinite dimensional quantum systems using covariance matrices of local observables. We show that these criteria are useful to detect a wide range of entangled states particularly in high dimensional systems and that the Gaussian steering criteria for general M x N-modes of continuous variables are obtained as a special case. Extending from the approach of entanglement detection via covariance matrices, our criteria are based on the local uncertainty principles incorporating the asymmetric nature of steering scenario. Specifically, we apply the formulation to the case of local orthogonal observables and obtain some useful criteria that can be straightforwardly computable, and testable in experiment, with no need for numerical optimization.